Title

Non-Crossing Matchings in the Annulus

Faculty Sponsor

Paul Drube

College

Arts and Sciences

Department/Program

Mathematics

Document Type

Poster Presentation

Celebration Date

Spring 5-2-2015

Abstract

The Catalan numbers are a sequence of integers that count various recursively-defined objects, as well as many structures that are important in mathematics and computer science. It is well known that the number of distinct non-crossing matchings on 2n points in the half-plane equals the nth Catalan number. Our work generalizes this notion of non-crossing matchings, as well as the circular matching of Golbach and Tijdeman, to non-crossing matchings in the annulus. We present results enumerating these annular matchings. We also develop interesting bijections between specific classes of annular matchings and well-studied mathematical objects such as combinatorial necklaces and planar graphs.

Biographical Information about Author(s)

Puttipong Pongtanapaisan is a senior mathematics/music major.

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